28.2.42 problem 42

Internal problem ID [4485]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 42
Date solved : Monday, January 27, 2025 at 09:21:07 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y&=96 x^{2} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 41

dsolve(diff(y(x),x$2)-4*y(x)=96*x^2*exp(2*x)+4*exp(-2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (32 x^{3}-24 x^{2}+4 c_{1} +12 x -3\right ) {\mathrm e}^{2 x}}{4}-{\mathrm e}^{-2 x} \left (x -c_{2} +\frac {1}{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.117 (sec). Leaf size: 48

DSolve[D[y[x],{x,2}]-4*y[x]==96*x^2*Exp[2*x]+4*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-2 x} \left (e^{4 x} \left (32 x^3-24 x^2+12 x-3+4 c_1\right )-4 x-1+4 c_2\right ) \]